An upper bound for a valence of a face in a parallelohedral tiling

作者：Magazinov Alexander^*

来源：European Journal of Combinatorics, 2013, 34(7): 1108-1113.

DOI：10.1016/j.ejc.2013.02.004

Consider a face-to-face parallelohedral tiling of R-d and a (d - k)-dimensional face F of the tiling. We prove that the valence of F (i.e. the number of tiles containing F as a face) is not greater than 2(k). If the tiling is affinely equivalent to a Voronoi tiling for some lattice (the so called Voronoi case), this gives a well-known upper bound for the number of vertices of a Delaunay k-cell. Yet we emphasize that such an affine equivalence is not assumed in the proof.

• 出版日期2013-10